Ms M.E. Sáiz Pérez: "Game Theory at Work: OR models and algorithms to solve multi-actor heterogeneous decision problems"

The objective of this thesis is to explore the potential of combining Game Theory (GT) models with Operations Research (OR) modelling. This includes development of algorithms to solve these complex OR models for different empirical situations. The challenge is to get GT “at work” by applying such models and techniques to practical cases.  Four different cases with a challenge on the development of algorithms are studied.  A first case illustrates a multiple coalition formation game in which membership rules and different transfer schemes are described. The goal is to develop methods for checking stability of coalition structures. A new mathematical programming formulation, crucial for the development of the algorithms, is elaborated. Available data is used to determine which stable coalitions appear and which procedures can be used to make coalitions stable. Also the influence of membership rules (whether actors are free to become a member) is investigated.  A second case studies a model of coalition formation in politics with n parties trying to form a government. Given the number of parties and policy dimension m (number of items), computational algorithms are developed to compute all possible majority coalitions and preferences of parties over those coalitions. Application to Dutch data and theoretical examples leads to testing of hypotheses with surprising results with respect to coalition formation. A third case describes a two-stage location-quantity game where n>2 firms are competing on m>2 markets. The space where the firms can locate are nodes on a network. Analytical solutions for the supplying decisions and properties for determining the number of suppliers to each market are derived. In finding the equilibria, a complete enumeration algorithm and a local search algorithm are used. Two cases are elaborated to illustrate the procedures and the analytical results. The last case deals with a competitive facility location problem in which the concept of Stackelberg leader-follower problem is applied. The follower problem and leader problem are global optimisation problems. Branch-and-Bound (B&B) algorithms that guarantee to find the optimum of both problems are designed.